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Let S be partitioned into r×s disjoint sets E_i and F_j where the general subset is denoted E_i intersection F_j. Then the marginal probability of E_i is ...

The Galton board, also known as a quincunx or bean machine, is a device for statistical experiments named after English scientist Sir Francis Galton. It consists of an ...

Let a distribution to be approximated be the distribution F_n of standardized sums Y_n=(sum_(i=1)^(n)(X_i-X^_))/(sqrt(sum_(i=1)^(n)sigma_X^2)). (1) In the Charlier series, ...

Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...

The mean of a distribution with probability density function P(x) is the first raw moment mu_1^', defined by mu=<x>, (1) where <f> is the expectation value. For a continuous ...

Sigma is the eighteenth letter of the ancient Greek alphabet. As an upper case letter (Sigma), it is used as a symbol for sums and series. As a lower case letter (sigma) it ...

A confidence interval is an interval in which a measurement or trial falls corresponding to a given probability. Usually, the confidence interval of interest is symmetrically ...

An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...

Let S_n be the sum of n random variates X_i with a Bernoulli distribution with P(X_i=1)=p_i. Then sum_(k=0)^infty|P(S_n=k)-(e^(-lambda)lambda^k)/(k!)|<2sum_(i=1)^np_i^2, ...

The Lorentzian function is the singly peaked function given by L(x)=1/pi(1/2Gamma)/((x-x_0)^2+(1/2Gamma)^2), (1) where x_0 is the center and Gamma is a parameter specifying ...